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The commutative property is a property of some Binary operations. A binary operation is commutative if and only if the order in which it is done does not change the result. For example, multiplication has the commutative property: xy=yx.

In propositional logic, it is a valid rule of inference consisting of two subrules:

P \wedge Q \Leftrightarrow Q \wedge P

P \vee Q \Leftrightarrow Q \vee P

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